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anastassius [24]
2 years ago
13

A right circular cylinder is changing shape. The radius is decreasing at the rate of 2 inches/sec while it's height is increasin

g at the rate of 5 inches/sec. When the radius is 4 inches and the height is 6 inches, how fast is the volume changing? Round your answer to three decimal places
Mathematics
1 answer:
Savatey [412]2 years ago
7 0

Answer:

<h3> 552.640in³/s</h3>

Step-by-step explanation:

Volume of a cylinder is expressed as;

V = \pi r^2 h

\frac{dV}{dt} = \frac{dV}{dr} \frac{dr}{dt} +\frac{dV}{dh} \frac{dh}{dt}

dV/dr = 2πrh

dV/dr = 2π(4)(6)

dV/dr = 48(3.14)

dV/dr = 150.72in³/m

dV/dh = πr²

dV/dh = 3.14(4)²

dV/dh = 50.24

Given

dh/dt = 5in/s

dr/dt = 2in/s

Substitute into the dV/dt

dV/dt = 150.72(2)+50.24(5)

dV/dt = 301.44 + 251.2

dV/dt= 552.640in³/s

The volume is changing at the rate of  552.640in³/s

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